TRES-package: Tensor Regression with Envelope Structure

In TRES: Tensor Regression with Envelope Structure

Description

Provides the ordinary least squares estimator and the three types of tensor envelope structured estimators for tensor response regression (TRR) and tensor predictor regression (TPR) models. The three types of tensor envelope structured approaches are generic and can be applied to any envelope estimation problems. The full Grassmannian (FG) optimization is often associated with likelihood-based estimation but requires heavy computation and good initialization; the one-directional optimization approaches (1D and ECD algorithms) are faster, stable and does not require carefully chosen initial values; the SIMPLS-type is motivated by the partial least squares regression and is computationally the least expensive.

Author(s)

Wenjing Wang, Jing Zeng and Xin Zhang

References

Zeng J., Wang W., Zhang X. (2021) TRES: An R Package for Tensor Regression and Envelope Algorithms. Journal of Statistical Software, 99(12), 1-31. doi:10.18637/jss.v099.i12.

Cook, R.D. and Zhang, X. (2016). Algorithms for envelope estimation. Journal of Computational and Graphical Statistics, 25(1), pp.284-300.

Li, L. and Zhang, X. (2017). Parsimonious tensor response regression. Journal of the American Statistical Association, 112(519), pp.1131-1146.

Zhang, X. and Li, L. (2017). Tensor envelope partial least-squares regression. Technometrics, 59(4), pp.426-436.

Cook, R.D. and Zhang, X. (2018). Fast envelope algorithms. Statistica Sinica, 28(3), pp.1179-1197.

See Also

Useful links:

• https://github.com/leozeng15/TRES

• Report bugs at https://github.com/leozeng15/TRES/issues

Examples

library(TRES)
## Load data "bat"
data("bat")
x <- bat$x
y <- bat$y

## 1. Fitting with OLS method.
fit_ols <- TRR.fit(x, y, method="standard")

## Print cofficient
coef(fit_ols)

## Print the summary
summary(fit_ols)

## Extract the mean squared error, p-value and standard error from summary
summary(fit_ols)$mse
summary(fit_ols)$p_val
summary(fit_ols)$se

## Make the prediction on the original dataset
predict(fit_ols, x)

## Draw the plots of two-way coefficient tensor (i.e., matrix) and p-value tensor.
plot(fit_ols)

## 2. Fitting with 1D envelope algorithm. (time-consuming)

fit_1D <- TRR.fit(x, y, u = c(14,14), method="1D") # pass envelope rank (14,14)
coef(fit_1D)
summary(fit_1D)
predict(fit_1D, x)
plot(fit_1D)

TRES documentation built on Oct. 20, 2021, 9:06 a.m.